I don't think there is a question whether or not there is a traveling wavein the cochlea. Fluid mechanics dictates that there has to be one.

There has to be one, if a volume shift of cochlear fluids occurs. Such a volume shift apparently occurs at high sound levels (>60 dB SPL). However, to induce sound waves in the cochlear fluids and also a hair cell response there is no need at all for a volume shift. This was recently demonstrated by Huber et al. (2008) in a series of elegant experiments:

In other words, sound waves can enter the cochlea and excite hair cells without a fluid displacement and without causing a traveling wave.

Sorry, I did not state that there had to be bet influx at the stapes or a volume shift a you name it. Any fluid motion (such as caused by a rocking stapes) will cause a travelling wave. Even the minute fluid displacements in a compession wave will cause a traveling wave.

The problem I see with a compression wave being the stimulus and the

haircells acting as pressure sensors .....

Hair cells need not be pressure sensors for a response to sound waves (compression waves). The "hairs" of the hair cells can act as wave detectors. Already today we see that they apparently do this in lizard ears. Manley (2006) measured spontaneous otoacoustic emissions (SOAEs) from ten lizard species that have no tectorial membranes. In these animals free-standing hair bundles vibrate through their own motor mechanism and thereby produce sound waves in the inner ear fluids that are measurable from the outside. There is no reason why this process should not work in reverse as well, such that hair bundles respond to sound waves that have entered the inner ear fluids from the outside.

I am sure hair bundles can move and serve as wave detectors. As a matter of fact I strongly support that view. This implies that there is fluid motion which stimulates the hair cells. And as I said before, fluid motion implies a traveling wave.

A tectorial membrane is not necessary to get fluid motion. There can be fluid motion without a membrane. But if there is both fluid motion and a membrane there will be a traveling wave.